Using fractional integrals properties, a thermodynamical fractional variational principle δ(Dω(-1-1/k)ρ(ω)) = 0 is deduced. The fractal character is due to the non-differentiable nature of the microscopic level. Our results show that statistical thermodynamics is a variational theory. In this respect, another definition of the entropy is introduced.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.